Finite Group Databasebeta

← Prev (#11755742) Next (#11755744) →

C3×#66066 #11755743

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#66066

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ #556
SylowC5 ⋊ C3×#556

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×D20C22
hypercenterC3×C4⋊Q8D5
hypocenterC5C3×#556
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3)(4,5,7,8,6)(9,12,13,11)(10,16,15,14)(17,19,20,23)(18,22,21,24);(10,15)(11,12)(17,18,20,21)(19,24,23,22);(9,11,13,12)(10,14,15,16);(5,6)(7,8)(9,10)(11,14)(12,16)(13,15)(18,21)(19,23)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601990, C3×#10599226, #14289301, …
maximal normal subgroup ofC3×#10601990, C3×#10599226, #14289301, …
maximal quotient ofC3×#10607711, C3×#10606055, C3×#10606056, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9938);